Discretization of the Density Matrix as a Nonlinear Positive Map and Entanglement
- Authors: López-Saldívar J.A.1, Figueroa A.1, Castaños O.1, López–Peña R.1, Man’ko M.A.2, Man’ko V.I.2,3
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Affiliations:
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México
- Lebedev Physical Institute, Russian Academy of Sciences
- Moscow Institute of Physics and Technology (State University)
- Issue: Vol 37, No 4 (2016)
- Pages: 313-327
- Section: Article
- URL: https://journal-vniispk.ru/1071-2836/article/view/247892
- DOI: https://doi.org/10.1007/s10946-016-9578-4
- ID: 247892
Cite item
Abstract
We propose the discretization of the density matrix as a nonlinear positive map for systems with continuous variables. We use this procedure for calculating the entanglement between two modes through different criteria, such as Tsallis entropy, von Neumann entropy and linear entropy, and the logarithmic negativity. As an example, we study the dynamics of entanglement for the two-mode squeezed-vacuum state in the parametric amplifier and show good agreement with the analytic results. Also we address the loss of information on the system state due to the discretization of the density matrix.
About the authors
Julio A. López-Saldívar
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México
Author for correspondence.
Email: julio.lopez@nucleares.unam.mx
Mexico, Apdo. Postal 70-543, México, D.F., 04510
Armando Figueroa
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México
Email: julio.lopez@nucleares.unam.mx
Mexico, Apdo. Postal 70-543, México, D.F., 04510
Octavio Castaños
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México
Email: julio.lopez@nucleares.unam.mx
Mexico, Apdo. Postal 70-543, México, D.F., 04510
Ramón López–Peña
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México
Email: julio.lopez@nucleares.unam.mx
Mexico, Apdo. Postal 70-543, México, D.F., 04510
Margarita A. Man’ko
Lebedev Physical Institute, Russian Academy of Sciences
Email: julio.lopez@nucleares.unam.mx
Russian Federation, Leninskii Prospect 53, Moscow, 119991
Vladimir I. Man’ko
Lebedev Physical Institute, Russian Academy of Sciences; Moscow Institute of Physics and Technology (State University)
Email: julio.lopez@nucleares.unam.mx
Russian Federation, Leninskii Prospect 53, Moscow, 119991; Dolgoprudnyi, Moscow Region, 141700
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